
from manim import *
class math(MovingCameraScene):
    def construct(self):
        self.camera.background_color = BLACK  # 设置背景颜色
        self.camera.frame_width = 100  # 设置边框宽度
        self.camera.frame_height = 60  # 设置边框高度
        self.camera.pixel_height = 1080  # 设置像素高度
        self.camera.pixel_width = 1920  # 设置像素宽度
        self.camera.center = ORIGIN  # 设置中心点位置
        self.camera.scale_factor = 1.0  # 设置缩放因子
        #设置横线
        for i in range(60*2+1):       
            dot1=Dot([-500,5*(i-60),0]).set_opacity(0.5)
            dot2=Dot([500,5*(i-60),0]).set_opacity(0.5)
            if i==6:
                line1=Line(dot1,dot2).set_color(WHITE).set_opacity(0.5)
                
            else:
                line1=Line(dot1,dot2).set_color(WHITE).set_opacity(0.5)
               
            self.add(dot1,dot2,line1)
        #设置竖线
        for i in range(100*2+1):        
            dot3=Dot([(i-100)*5,-300,0]).set_opacity(0.5)
            dot4=Dot([(i-100)*5,300,0]).set_opacity(0.5)
            if i==10:
                line2=Line(dot3,dot4).set_color(WHITE).set_opacity(0.5)
                
            else:
                line2=Line(dot3,dot4).set_color(WHITE).set_opacity(0.5)
            self.add(dot3,dot4,line2)
        #设置三个点
        dot1 = Dot(radius=1, color=RED)  
        dot1.move_to([-47.5,27.5,0]) 
        dot2 = Dot(radius=1, color=YELLOW)  
        dot2.move_to([-42.5,27.5,0])  
        dot3 = Dot(radius=1, color=GREEN)  
        dot3.move_to([-37.5,27.5,0])
        #镜头跟进效果 
        self.camera.frame.save_state()
        #题目出现
        text = Tex(r"\text{(2019年)求曲线}$y=e^{-x}\sin x ( x\geq  0) $\text{与X轴之间的面积}"
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,0,0])
        
        self.play(Write(text),self.camera.frame.animate.scale(0.8))
        self.wait()
        #镜头拉回
          #分析文本
        #text100=MarkupText("<b><i>分析/解：</i></b>",color=PINK).scale(5.0).move_to([-38,12.5,0])
        self.play(Restore(self.camera.frame))
        self.play(FadeIn(dot1),run_time=0.1)
        self.play(FadeIn(dot2),run_time=0.1)
        self.play(FadeIn(dot3),run_time=0.1)
        #题目向上移动
        self.play(text.animate().move_to([0,20,0]) )
        rectangle=Rectangle(color=BLUE,fill_opacity=0.3,width=70,height=5
                            ,stroke_color=BLUE,stroke_width=20)
        rectangle.move_to([0, 20, 0])
        self.play(Create(rectangle))
        
        text1 = Tex(r"\text{面积S}$=\int _{a}^{b}\left| f\left( x\right) \right| dx $"
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,12,0])
        
        self.play(Write(text1))

        text2 = Tex(r"$S=\int _{0}^{+\infty }\left| e^{-x}\sin x\right| dx$"
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,12,0])
        
        self.play(ReplacementTransform(text1,text2))
        self.wait(0.2)
        rectangle1=Rectangle(color=GREEN,fill_opacity=0.3,width=30,height=5
                            ,stroke_color=GREEN,stroke_width=20)
        rectangle1.move_to([0, 12, 0])
        self.play(Create(rectangle1))
        self.play(FadeOut(rectangle1))
        
        #下划线
        dot1=Dot([-1,10,0])
        dot2=Dot([9,10,0])
        line=Line(dot1,dot2).set_color(YELLOW)
        line.set_stroke(width=30)  # 设置宽度为 30
        self.play(Create(line))
        text3 = Tex(r"$S=\int _{0}^{+\infty } e^{-x}\left|\sin x\right| dx$"
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,12,0])
        
        self.play(ReplacementTransform(text2,text3),FadeOut(line))
        self.wait(0.2)

        rectangle2=Rectangle(color=GREEN,fill_opacity=0.3,width=4.5,height=5
                            ,stroke_color=GREEN,stroke_width=20)
        rectangle2.move_to([-5, 12, 0])
        rectangle3=Rectangle(color=GREEN,fill_opacity=0.3,width=4.5,height=5
                            ,stroke_color=GREEN,stroke_width=20)
        rectangle3.move_to([-5, 12, 0])
        self.play(Create(rectangle2),Create(rectangle3))
        
        text4 = Tex(r"$\displaystyle \sum ^{\infty }_{n=0}\int ^{\left( n+1\right) \pi }_{n\pi }e^{-x}\left| \sin x\right| dx$"
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,4,0])
        
        self.play(ReplacementTransform(rectangle3,text4))
        self.wait(0.2)
        rectangle4=Rectangle(color=GREEN,fill_opacity=0.3,width=14,height=8
                            ,stroke_color=GREEN,stroke_width=20)
        rectangle4.move_to([-8, 4, 0])
        self.play(Create(rectangle4))
        text5 = Tex(r"$\left| \sin x\right| =\left( -1\right) ^{n}\sin x$",color=YELLOW
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([30,4,0])
        self.play(Create(text5))
        text6 = Tex(r"$\displaystyle \sum ^{\infty }_{n=0}\int ^{\left( n+1\right) \pi }_{n\pi }\left( -1\right) ^{n}e^{-x}\sin xdx$"
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,4,0])
        
        self.play(ReplacementTransform(text5,text6),ReplacementTransform(text4,text6),FadeOut(rectangle4))
        self.wait(0.2)

        text7 = Tex(r"$\displaystyle \sum ^{\infty }_{n=0}\left( -1\right) ^{n}\cdot \int ^{\left( n+1\right) \pi }_{n\pi }e^{-x}\sin xdx$"
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,4,0])
        
        self.play(ReplacementTransform(text6,text7))
        self.wait(0.2)
        rectangle5=Rectangle(color=RED,fill_opacity=0.3,width=23,height=8
                            ,stroke_color=RED,stroke_width=20)
        rectangle5.move_to([6, 4, 0])
        self.play(Create(rectangle5))
        text8 = Tex(r"$ \int e^{-x}\sin xdx$",color=YELLOW
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([6,-5,0])
        self.play(Create(text8))
        text9 = Tex(r"$ =\dfrac{-\left( \sin x+\cos x\right) }{2}\cdot e^{-x}+C$",color=WHITE
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).next_to(text8,RIGHT,buff=1)
        self.play(Create(text9))
        text10 = Tex(r"\text{带入}$ \int _{n\pi }^{\left( n+1\right) \pi }$",color=WHITE
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([20,-12,0])
        self.play(Create(text10))
        text11 = Tex(r"$ \int _{n\pi }^{\left( n+1\right) \pi }e^{-x}\sin xdx=\dfrac{\left( -1\right) ^{n}e^{-\left( n+1\right) \pi }}{2}\cdot \left[ 1+e^{\pi }\right] $",color=YELLOW
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([6,-5,0])
        self.play(ReplacementTransform(text10,text11),ReplacementTransform(text9,text11),ReplacementTransform(text8,text11))
        self.wait(0.2)
        
        text12 = Tex(r"$\dfrac{1+e^{\pi }}{2}\cdot \displaystyle \sum ^{\infty }_{n=0}e^{-\left( n+1\right) \pi }$",color=WHITE
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,-6,0])
        
        self.play(ReplacementTransform(text11,text12))
        self.wait(0.2)
        rectangle6=Rectangle(color=YELLOW,fill_opacity=0.3,width=14,height=8
                            ,stroke_color=YELLOW,stroke_width=20)
        rectangle6.move_to([5, -6, 0])
        self.play(Create(rectangle6))
        text13 = Tex(r"$e^{-\pi }+e^{-2\pi }+\ldots +e^{-\left( n+1\right) \pi }+\ldots $",color=WHITE
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,-12.5,0])
        
        self.play(ReplacementTransform(rectangle6,text13))
        self.wait(0.2)
        #下划线
        dot1=Dot([-19,-15,0])
        dot2=Dot([15,-15,0])
        line=Line(dot1,dot2).set_color(YELLOW)
        line.set_stroke(width=30)  # 设置宽度为 30
        self.play(Create(line))
        #框框移动
        self.play(text13.animate().move_to([-25,-12.5,0]),FadeOut(line))
        text14 = Tex(r"$= \lim\limits _{n\rightarrow \infty }\dfrac{e^{-\pi }\left( 1-e^{-\left( n+1\right) \pi }\right) }{1-e^{-\pi }}$",color=WHITE
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).next_to(text13,RIGHT,buff=1)
        
        self.play(Write(text14))
        self.wait(0.2)
        rectangle7=Rectangle(color=YELLOW,fill_opacity=0.3,width=9,height=3
                            ,stroke_color=YELLOW,stroke_width=20)
        rectangle7.move_to([18, -11, 0])
        self.play(Create(rectangle7))
        text15 = Tex(r"$\lim\limits _{n\rightarrow \infty }e^{-\left( n+1\right) \pi }=0 $",color=YELLOW
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([30,-5,0])
        
        self.play(ReplacementTransform(rectangle7,text15))
        self.wait(0.2)
        text16 = Tex(r"$=\dfrac{e^{-\pi }}{1-e^{-\pi }}$",color=YELLOW
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).next_to(text14,RIGHT,buff=1)
        
        self.play(ReplacementTransform(text15,text16))
        self.wait(0.2)
        text17 = Tex(r"$=\dfrac{1}{2}\cdot \dfrac{e^{\pi }+1}{e^{\pi }-1}$",color=YELLOW
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).next_to(text12,RIGHT,buff=1)
        
        self.play(ReplacementTransform(text16,text17),ReplacementTransform(text14,text17),ReplacementTransform(text13,text17))
        self.wait(0.2)
        self.wait()